CN111460732A - A Construction Method of Nonlinear Model of Planar Motor - Google Patents

Abstract

The invention discloses a method for constructing a non-linear model of a plane motor. The method establishes a non-linear dynamic model of the plane motor, and establishes a neural network model based on the non-linear dynamic model of the plane motor; The neural network model is trained; the model parameters of the trained neural network model are used as the model parameters of the nonlinear dynamic model of the planar motor to obtain the nonlinear dynamic model of the planar motor. In the present invention, the plane motor model is a nonlinear dynamic model, which reflects the nonlinear dynamic characteristics of the plane motor, and the model has high precision; the model parameters of the plane motor nonlinear model are solved through the neural network model, which improves the credibility of the model. degree, so that it can be used in the controller of the planar motor to improve the accuracy of the position control of the planar motor.

Description

A Construction Method of Nonlinear Model of Planar Motor

technical field

The invention relates to the technical field of planar motors, in particular to a method for constructing a nonlinear model of a planar motor.

Background technique

Planar motors have the advantages of simple structure, convenient installation, good heat dissipation, high precision, high speed, low cost and high reliability, and have great application prospects in the field of precision manufacturing. At present, high-precision position control is the focus of the planar motor field. The accuracy of the mathematical model of the planar motor seriously affects its high-precision operation. In addition, the highly nonlinear characteristics of the planar motor greatly hinder its accurate modeling.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a method for constructing a nonlinear model of a planar motor in view of the deficiencies of the prior art.

In order to solve the above-mentioned technical problems, the technical scheme adopted in the present invention is as follows:

A method for constructing a nonlinear model of a planar motor, the method comprising:

establishing a nonlinear dynamic model of the planar motor, and establishing a neural network model based on the nonlinear dynamic model of the planar motor, wherein the model parameters of the neural network model are model parameters of the nonlinear dynamic model of the planar motor;

training the neural network model based on a preset training sample set;

The model parameters of the trained neural network model are used as the model parameters of the nonlinear dynamic model of the planar motor to obtain the nonlinear dynamic model of the planar motor.

The method for constructing a nonlinear model of a planar motor, wherein the preset training sample set includes several training samples, and each training sample includes training data and real state information corresponding to the training data, wherein the training data includes a state information and control.

In the method for constructing a nonlinear model of a planar motor, the real state information is the state information of the training data at the next moment, wherein the state information includes speed information and position information.

The method for constructing the nonlinear model of the planar motor, wherein the training of the neural network model based on a preset training sample set specifically includes:

Inputting the training data into the neural network model, and extracting the predicted state information of the training data through the neural network model;

determining a loss function corresponding to the training data based on the predicted state information and the actual state information corresponding to the training data;

The neural network model is trained based on the loss function.

The construction method of the nonlinear model of the plane motor, wherein the neural network model includes a mapping unit and a linear transformation unit; the training data is input into the neural network model, and the predicted state of the training data is extracted through the neural network model The information specifically includes:

Inputting the state information into the mapping unit, and outputting coupling parameters through the mapping unit;

The coupling parameter and the control amount are input into the linear transformation unit, and the predicted state information of the training data is output through the linear transformation unit.

The method for constructing the nonlinear model of the planar motor, wherein the loss function is:

Among them, J is the loss function, x _{real_l} (k) is the real state information, x _l (k) is the predicted state information, and k represents the kth time.

The described establishment of the nonlinear dynamic model of the planar motor is as follows:

x_l1(k)为l轴k时刻的位置信息，x_l2(k)为l轴k时刻的速度信息，y_l(k)为k时刻模型输出的位置信息，C_l＝[1 0]，G_l和H_l为l轴的系数矩阵，F_l[x_l(k)]为l轴的非线性状态向量，u_l(k)为控制量，

x_l1(k+1)为l轴k+1时刻的位置信息，x_l2(k+1)为l轴k+1时刻的速度信息。in,

x _l1 (k) is the position information of the l-axis at time k, x _l2 (k) is the velocity information of the l-axis at time k, y _l (k) is the position information output by the model at time k, C _l =[1 0], G _l and H _l are the coefficient matrix of the l-axis, F _l [x _l (k)] is the nonlinear state vector of the l-axis, u _l (k) is the control quantity,

x _l1 (k+1) is the position information at the time k+1 of the l-axis, and x _l2 (k+1) is the velocity information at the time of the l-axis k+1.

A control method for a planar motor, using the method for constructing a nonlinear model of a planar motor as described above to construct a nonlinear model of a planar motor, the method comprising:

Based on the nonlinear model of the planar motor, determining that the planar motor at the next moment is the desired position information;

determining the control amount of the planar motor based on the desired position information and the actual position information of the planar motor;

The control amount is applied to the planar motor to control the planar motor.

A computer-readable storage medium storing one or more programs, the one or more programs can be executed by one or more processors to implement the planar motor as described in any of the above Steps in a method for building a nonlinear model.

A terminal device, comprising: a processor, a memory and a communication bus; a computer-readable program executable by the processor is stored on the memory;

The communication bus implements connection communication between the processor and the memory;

When the processor executes the computer-readable program, the steps in the method for constructing a nonlinear model of a planar motor as described above are implemented.

Beneficial effects: compared with the prior art, the present invention provides a method for constructing a nonlinear model of a planar motor, the method establishes a nonlinear dynamic model of a planar motor, and a neural network model is established based on the nonlinear dynamic model of the planar motor ; Train the neural network model based on a preset training sample set; use the model parameters of the trained neural network model as the model parameters of the nonlinear dynamic model of the planar motor to obtain the nonlinear dynamic model of the planar motor. In the present invention, the plane motor model is a nonlinear dynamic model, which reflects the nonlinear dynamic characteristics of the plane motor, and the model has high precision; the model parameters of the plane motor nonlinear model are solved through the neural network model, which improves the credibility of the model. degree, so that it can be used in the controller of the planar motor to improve the accuracy of the position control of the planar motor.

Description of drawings

FIG. 1 is a flowchart of a method for constructing a nonlinear model of a planar motor provided by the present invention.

FIG. 2 is a schematic diagram of a planar motor control system in a method for constructing a nonlinear model of a planar motor provided by the present invention.

3 is a schematic diagram of a training process of a neural network model in the method for constructing a nonlinear model of a planar motor provided by the present invention.

FIG. 4 is a schematic structural diagram of an embodiment of a neural network model in the method for constructing a nonlinear model of a planar motor provided by the present invention.

FIG. 5 is a schematic structural diagram of another embodiment of a neural network model in the method for constructing a nonlinear model of a planar motor provided by the present invention.

FIG. 6 is a schematic structural diagram of a terminal device provided by the present invention.

Detailed ways

The present invention provides a method for constructing a nonlinear model of a planar motor. In order to make the purpose, technical solutions and effects of the present invention clearer and clearer, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

It will be understood by those skilled in the art that the singular forms "a", "an", "the" and "the" as used herein can include the plural forms as well, unless expressly stated otherwise. It should be further understood that the word "comprising" used in the description of the present invention refers to the presence of stated features, integers, steps, operations, elements and/or components, but does not exclude the presence or addition of one or more other features, Integers, steps, operations, elements, components and/or groups thereof. It will be understood that when we refer to an element as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Furthermore, "connected" or "coupled" as used herein may include wirelessly connected or wirelessly coupled. As used herein, the term "and/or" includes all or any element and all combination of one or more of the associated listed items.

It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It should also be understood that terms, such as those defined in a general dictionary, should be understood to have meanings consistent with their meanings in the context of the prior art and, unless specifically defined as herein, should not be interpreted in idealistic or overly formal meaning to explain.

This embodiment provides a method for constructing a nonlinear model of a planar motor, and the method can be applied to an electronic device having a front-facing camera or a rear-facing camera function, and the electronic device can be implemented in various forms. For example, a mobile phone, a tablet computer, a palmtop computer, a personal digital assistant (Personal Digital Assistant, PDA) and the like. In addition, the functions implemented by the method can be implemented by a processor in the electronic device calling program codes, and of course the program codes can be stored in a computer storage medium. It can be seen that the electronic device includes at least a processor and a storage medium.

As shown in FIG. 1 , this implementation provides a method for constructing a nonlinear model of a planar motor, and the method may include the following steps:

S10. Establish a nonlinear dynamic model of the planar motor, and establish a neural network model based on the nonlinear dynamic model of the planar motor, wherein the model parameters of the neural network model are model parameters of the nonlinear dynamic model of the planar motor.

Specifically, the nonlinear dynamic model of the planar motor is a model established based on control variables and state information, and the nonlinear dynamic model of the planar motor includes a state equation and an output equation. The state equation is used to estimate the state information of the planar motor at the next moment, and the output equation is used to output the position information of the current moment. Wherein, the control quantity is the output quantity of the controller in the planar motor control system (for example, the planar motor control system shown in FIG. 2 ), and the state information includes speed information and position information.

The nonlinear dynamic model of the planar motor established based on the control variables and state information may be:

x_l1(k)为l轴k时刻的位置信息，x_l2(k)为l轴k时刻的速度信息，y_l(k)为k时刻模型输出的位置信息，C_l＝[1 0]，G_l和H_l为l轴的系数矩阵，F_l[x_l(k)]为l轴的非线性状态向量，u_l(k)为控制量，

x_l1(k+1)为l轴k+1时刻的位置信息，x_l2(k+1)为l轴k+1时刻的速度信息。in,

x _l1 (k) is the position information of the l-axis at time k, x _l2 (k) is the velocity information of the l-axis at time k, y _l (k) is the position information output by the model at time k, C _l =[1 0], G _l and H _l are the coefficient matrix of the l-axis, F _l [x _l (k)] is the nonlinear state vector of the l-axis, u _l (k) is the control quantity,

x _l1 (k+1) is the position information at the time k+1 of the l-axis, and x _l2 (k+1) is the velocity information at the time of the l-axis k+1.

Further, in an implementation manner of this embodiment, the nonlinear state vector F _l [x _l (k)] of the l-axis is used to represent the nonlinear characteristics of the nonlinear dynamic model of the planar motor, and through the nonlinear characteristics It can reflect the nonlinear dynamic characteristics of the planar motor and improve the model accuracy. Wherein, the expression of the nonlinear state vector F _l [x _l (k)] of the l-axis may be:

Among them, A _l1 , A _l2 and a _l are the gain coefficients of the l-axis, D _l [x _l1 (k)] and D _l [x _l12 (k)] are the coupling functions of the l-axis, and the coupling functions are used for Representing the coupling characteristics of the nonlinear dynamic model of a planar motor, the D _l [x _l (k)] and D _l [x _l12 (k)] are expressed as:

D _l1 [x _l (k)]=ω _l1 x _l (k)=ω _l11 x _X1 +ω _l12 x _X2 +ω _l13 x _Y1 +ω _l14 x _Y2

D _l2 [x _l (k)]=ω _l2 x _l (k)=ω _l21 x _X1 +ω _l22 x _X2 +ω _l23 x _Y1 +ω _l24 x _Y2

where ω _l1 and ω _l2 are the l gain vectors.

In addition, in an implementation of this embodiment, the nonlinear state vector F _l [x _l (k)] of the l-axis may also be one of the following formulas:

Among them, h _l is the width of the Gaussian kernel function, and _cl is the center point of the Gaussian kernel function.

Further, in an implementation manner of this embodiment, the neural network model is established based on the nonlinear dynamic model of the planar motor, and the model parameters of the neural network model are model parameters of the nonlinear dynamic model of the planar motor. The input item of the neural network model is the state information of the planar motor, and the output item of the neural network model is the position information of the planar motor at the next moment. It can be understood that the neural network model is established based on the state equation of the nonlinear dynamic model of the planar motor, and its input items are the control variables and state information in the state equation; the output item is the state equation to determine the desired state. The position information in the information, the model function corresponding to the neural network model is the nonlinear state vector F _l [x _l (k)] of the l-axis in the nonlinear dynamic model of the plane motor, and the model of the neural network model The parameters are the coefficient matrices G _l and H _l of the l-axis. Therefore, the training of the neural network model is to determine the coefficient matrices _G1 and _H1 of the nonlinear dynamic model of the planar motor for the model parameters _G1 and _H1 of the neural network model, so as to improve the performance of the planar motor. The model accuracy of the nonlinear dynamic model is improved, thereby improving the accuracy of the planar motor control based on the nonlinear dynamic model of the planar motor.

S20. Train the neural network model based on a preset training sample set.

Specifically, the preset training sample set includes several training samples, each training sample includes training data and real state information corresponding to the training data, and the training data includes state information and control quantities. The real state information is state information of the training data at the next moment, and the state information includes speed information and position information. Thus, the training sample data includes speed information at the current moment, position information at the current moment, and control amount information at the current moment, and the output item of the neural network model is the predicted state information at the next moment.

In an implementation manner of this embodiment, the acquisition process of the preset training sample set may be as follows: collecting five samples, each sample has different trajectories and speeds, and each sample contains at least 10,000 sets of sequence data, For example, taking the step size of 1ms as an example, data with a duration of at least 10s needs to be collected. In addition, one set of the five samples is used to train the neural network-based nonlinear dynamic model of the planar motor, and the remaining four sets of samples are used to test the neural network-based nonlinear dynamic model of the planar motor. In addition, each set of training data includes the l-axis control quantity, the l-axis position and the l-axis speed, where the l-speed is the speed calculated by the numerical differentiation algorithm based on the l-axis position, and the l-axis control quantity is the output of the controller in the planar motor control system. In this way, the nonlinear dynamic model of the planar motor reflects the constraint characteristics of actuator saturation through the control quantity output by the controller in the planar motor control system.

In an implementation manner of this embodiment, as shown in FIG. 3 , the training of the neural network model based on the preset training sample set specifically includes:

S21, input the training data into the neural network model, and extract the predicted state information of the training data through the neural network model;

S22, determining a loss function corresponding to the training data based on the predicted state information and the actual state information corresponding to the training data;

S23. Train the neural network model based on the loss function.

Specifically, the predicted state information is the expected state information at the next moment. For example, if the state information in the training data is the state information at time k, then the predicted state information is the expected state information at time k+1. It can be understood that the state information in the training data is k is to see the actual state information, the real state information is the actual state information at time k+1, and the predicted state information is the expected state at time k+1. information. Thus, a loss function corresponding to the training data can be determined based on the predicted state information and the real state information corresponding to the training data, and the neural network model can be trained by using the loss function.

In an optional embodiment, the expression of the loss function may be:

Among them, J is the loss function, x _{real_l} (k) is the real state information, x _l (k) is the predicted state information, and k represents the kth time.

Further, after the loss function is determined, the gradient descent method can be used for learning to modify the network parameters of the neural network model, to obtain model parameters that meet preset conditions, and then to obtain the plane motor nonlinear model parameters _G1 and H _l . The model parameter satisfies the preset condition that the loss function value is smaller than the preset threshold or the training times of the neural network model reaches the preset times threshold. In addition, since the coupling function in the nonlinear state vector F _l [x _l (k)] of the l-axis includes the coupling coefficient, when the network model is revised, the coupling coefficient is revised to improve the The accuracy of the nonlinear state vector F _l [x _l (k)] of the l axis, thereby improving the accuracy of the nonlinear dynamic model of the planar motor.

The adjustment formula of the G _l , H _l and the coupling coefficient ω _l can be:

G _l (k+1)=G _l (k)-ηE _l (k)F _l [x(k)]+α[G _l (k)-G _l (k-1)]

H _l (k+1)=H _l (k)-ηE _l (k)u _l (k)+α[H _l (k)-H _l (k-1)]

w _l11 (k+1)=w _l11 (k)-η{g ₁ (k)x ₁ (k)+g ₃ (k)x ₁ (k)}

w _l12 (k+1)=w _l12 (k)-η{g ₁ (k)x ₂ (k)+g ₃ (k)x ₂ (k)}

w _l13 (k+1)=w _l13 (k)-η{g ₁ (k)x ₃ (k)+g ₃ (k)x ₃ (k)}

w _l14 (k+1)=w _l14 (k)-η{g ₁ (k)x ₄ (k)+g ₃ (k)x ₄ (k)}

w _l21 (k+1)=w _l21 (k)-η{g ₂ (k)x ₁ (k)+g ₄ (k)x ₁ (k)}

w _l22 (k+1)=w _l22 (k)-η{g ₂ (k)x ₂ (k)+g ₄ (k)x ₂ (k)}

w _l23 (k+1)=w _{l23 (k)-η} {g ₂ (k)x ₃ (k)+g ₄ (k)x ₃ (k)}

w _l24 (k+1)=w _l24 (k)-η{g ₂ (k)x ₄ (k)+g ₄ (k)x ₄ (k)}

where η is the learning rate, α is the momentum factor, and g ₁ , g ₂ , g ₃ , and g ₄ are respectively

g ₁ (k)=E _l1 (k)G _l11 A _l1 a _l1 [1-f _l1 (x _l (k)) ² ]

g ₂ (k)=E _l1 (k)G _l12 A _l2 a _l2 [1-f _l2 (x _l (k)) ² ]

g ₃ (k)=E _l2 (k)G _l21 A _l1 a _l1 [1-f _l1 (x _l (k)) ² ]

g ₄ (k)=E _l2 (k)G _l22 A _l2 a _l2 [1-f _l2 (x _l (k)) ² ]

Further, in this embodiment, the neural network model includes a mapping unit and a linear transformation unit; the inputting the training data into the neural network model, and extracting the prediction state information of the training data through the neural network model specifically includes: :

Inputting the state information into the mapping unit, and outputting coupling parameters through the mapping unit;

The coupling parameter and the control amount are input into the linear transformation unit, and the predicted state information of the training data is output through the linear transformation unit.

Specifically, the linear transformation unit may include at least one hidden layer, and the number of nodes in the last hidden layer is greater than or equal to 2, and the coupling parameter and the control amount are calculated by the convolution layer through the l-axis. The nonlinear state vector F _l [x _l (k)] of , obtains predicted velocity information and position information. For example, as shown in Fig. 4, the linear transformation unit includes a convolution layer, when the number of nodes in the convolution layer is 2, F _l [x _l (k)]∈R ^2×1 , G _l ∈R ^{2 ×2} ; when the number of hidden layer nodes is n, F _l [x _l (k)]∈R ^n×1 , G _l ∈R ^2×n ; as shown in Figure 5, the hidden layer can be extended to the number of layers m, a neural network with n nodes in each layer. The specific values of m and n need to be determined according to the modeling requirements.

S30. Use the model parameters of the trained neural network model as the model parameters of the nonlinear dynamic model of the planar motor to obtain the nonlinear dynamic model of the planar motor.

Specifically, after the model parameters of the neural network model meet the preset conditions, obtain _G1 and H1 in the neural network model, and use _G1 and _H1 as the model parameters of the _nonlinear dynamic model of the planar motor, thereby improving the The nonlinear dynamic model accuracy and control performance of the planar motor are obtained, which is suitable for the controller design of the planar motor. In addition, the nonlinear dynamic model of the planar motor considers the coupling characteristics of the two-dimensional motion, and establishes an independent nonlinear dynamic model of the X-axis and the Y-axis, which improves the accuracy and control performance of the planar motor model, and simplifies the planar motor with coupling characteristics. Controller structure. At the same time, the nonlinear dynamic model of the planar motor adopts the control quantity output by the controller as the input item of the neural network model, so that the model parameters meet the constraint characteristic of nonlinear actuator saturation, improve the accuracy and control performance of the planar motor model, and simplify the consideration at the same time. The controller structure of the actuator saturation, the more nonlinear dynamic model of the planar motor is more suitable for the actual planar motor system.

Based on the method for constructing the nonlinear model of the planar motor described above, the present embodiment provides a control method for the planar motor. Methods include:

Based on the nonlinear model of the planar motor, determining that the planar motor at the next moment is the desired position information;

determining the control amount of the planar motor based on the desired position information and the actual position information of the planar motor;

The control amount is applied to the planar motor to control the planar motor.

Based on the above method for constructing a nonlinear model of a planar motor, this embodiment provides a computer-readable storage medium, where the computer-readable storage medium stores one or more programs, and the one or more programs can be stored by one or more A plurality of processors are executed to implement the steps in the method for constructing a nonlinear model of a planar motor as described in the above embodiments.

Based on the method for constructing the nonlinear model of the planar motor, the present invention also provides a terminal device, as shown in FIG. 6 , which includes at least one processor 20 ; a display screen 21 ; and a memory 22 , and also A Communications Interface 23 and a bus 24 may be included. The processor 20 , the display screen 21 , the memory 22 and the communication interface 23 can communicate with each other through the bus 24 . The display screen 21 is set to display a user guide interface preset in the initial setting mode. The communication interface 23 can transmit information. The processor 20 may invoke logic instructions in the memory 22 to perform the methods in the above-described embodiments.

In addition, the above-mentioned logic instructions in the memory 22 can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product.

As a computer-readable storage medium, the memory 22 may be configured to store software programs and computer-executable programs, such as program instructions or modules corresponding to the methods in the embodiments of the present disclosure. The processor 20 executes functional applications and data processing by running the software programs, instructions or modules stored in the memory 22, ie, implements the methods in the above embodiments.

The memory 22 may include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function; the storage data area may store data created according to the use of the terminal device, and the like. Additionally, memory 22 may include high-speed random access memory, and may also include non-volatile memory. For example, U disk, removable hard disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), magnetic disk or optical disk and other media that can store program codes, or temporary state storage medium.

In addition, the specific process of loading and executing the above-mentioned storage medium and the multiple instruction processor in the terminal device has been described in detail in the above-mentioned method, and will not be described one by one here.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that it can still be The technical solutions described in the foregoing embodiments are modified, or some technical features thereof are equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. A method for constructing a nonlinear model of a planar motor is characterized by comprising the following steps:

establishing a nonlinear dynamic model of a planar motor, and establishing a neural network model based on the nonlinear dynamic model of the planar motor, wherein model parameters of the neural network model are model parameters of the nonlinear dynamic model of the planar motor;

training the neural network model based on a preset training sample set;

and taking the model parameters of the trained neural network model as the model parameters of the nonlinear dynamic model of the planar motor to obtain the nonlinear dynamic model of the planar motor.

2. The method for constructing the nonlinear model of the planar motor according to claim 1, wherein the preset training sample set includes a plurality of training samples, each training sample includes training data and real state information corresponding to the training data, and the training data includes state information and a control quantity.

3. The method for constructing the nonlinear model of the planar motor according to claim 2, wherein the real state information is state information of a next moment of the training data, wherein the state information includes speed information and position information.

4. The method for constructing the nonlinear model of the planar motor according to claim 2 or 3, wherein the training of the neural network model based on the preset training sample set specifically includes:

inputting the training data into the neural network model, and extracting the prediction state information of the training data through the neural network model;

determining a loss function corresponding to the training data based on the predicted state information and the real state information corresponding to the training data;

training the neural network model based on the loss function.

5. The construction method of the nonlinear model of the planar motor according to claim 4, wherein the neural network model comprises a mapping unit and a linear transformation unit; inputting the training data into the neural network model, and extracting the predicted state information of the training data through the neural network model specifically comprises:

inputting the state information into the mapping unit, and outputting a coupling parameter through the mapping unit;

and inputting the coupling parameters and the control quantity into the linear transformation unit, and outputting the prediction state information of the training data through the linear transformation unit.

6. The method for constructing the nonlinear model of the planar motor according to claim 4, wherein the loss function is:

wherein J is a loss function, x_{real_l}(k) For true state information, x_l(k) To predict the state information, k denotes the kth time.

7. The method for constructing the nonlinear dynamic model of the planar motor according to claim 1, wherein the establishing the nonlinear dynamic model of the planar motor comprises the following steps:

wherein ,

x_l1(k) position information at time k on the l-axis, x_l2(k) Speed information at time k on the l-axis, y_l(k) Position information output for the model at time k, C_l＝[10]，G_l and H_lIs a coefficient matrix of the l-axis, F_l[x_l(k)]A non-linear state vector of the l-axis, u_l(k) In order to control the amount of the liquid,

x_l1(k +1) is position information of the time k +1 on the l-axis, x_l2(k +1) is velocity information at the time of the l-axis k + 1.

8. A method for controlling a planar motor, wherein the planar motor nonlinear model is constructed by applying the method for constructing a planar motor nonlinear model according to any one of claims 1 to 7, the method comprising:

determining expected position information of the planar motor at the next moment based on the nonlinear model of the planar motor;

determining a control amount of the planar motor based on the expected position information and actual position information of the planar motor;

and applying the control quantity to the planar motor to control the planar motor.

9. A computer-readable storage medium storing one or more programs, which are executable by one or more processors, to implement the steps in the method for constructing a nonlinear model of a planar motor according to any one of claims 1 to 7.

10. A terminal device, comprising: a processor, a memory, and a communication bus; the memory has stored thereon a computer readable program executable by the processor;

the communication bus realizes connection communication between the processor and the memory;

the processor, when executing the computer readable program, implements the steps in the method of constructing a nonlinear model of a planar motor according to any one of claims 1 to 7.

Images